E. V. Ferapontov, K. R. Khusnutdinova, M. V. Pavlov, “Classification of Integrable <nobr>$(2+1)$</nobr>-Dimensional Quasilinear Hierarchies”, TMF, 2005, Volume 144, Number 1,Pages <nobr>35

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Classification of Integrable $(2+1)$-Dimensional Quasilinear Hierarchies

E. V. Ferapontov^ab, K. R. Khusnutdinova^bc, M. V. Pavlov^b

^a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
^b Loughborough University
^c Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences

Abstract: We investigate the $(2+1)$-dimensional hierarchies associated with the integrable PDEs of the form $\Omega_{tt}=F(\Omega_{xx},\Omega_{xt},\Omega_{xy})$, which generalize the dispersionless KP hierarchy. Integrability is understood as the existence of infinitely many hydrodynamic reductions.

Keywords: integrable hierachies of dKP type, hydrodynamic reductions, pseudopotentials.

DOI: 10.4213/tmf1829